Ronald White

Recent advances in the application of Boltzmann equation and fluid equation methods to charged particle transport in non-equilibrium plasmas

The kinetic theory of charged particles in gases has come a long way in the last 60 years or so, but many of the advances have yet to find their way into contemporary studies of low-temperature plasmas. This review explores the way in which this gap might be bridged, and focuses in particular on the analytic framework and numerical techniques for the solution of Boltzmanns equation for both electrons and ions, as well as on the development of fluid models and semi-empirical formulae. Both hydrodynamic and non-hydrodynamic regimes are considered and transport properties are calculated in various configurations of dc and ac electric and magnetic fields. We discuss in particular the duality in transport coefficients arising from non-conservative collisions (attachment, ionization).

Photocarrier drift distance in organic solar cells and photodetectors

Light harvesting systems based upon disordered materials are not only widespread in nature, but are also increasingly prevalent in solar cells and photodetectors. Examples include organic semiconductors, which typically possess low charge carrier mobilities and Langevin-type recombination dynamics – both of which negatively impact the device performance. It is accepted wisdom that the “drift distance” (i.e., the distance a photocarrier drifts before recombination) is defined by the mobility-lifetime product in solar cells. We demonstrate that this traditional figure of merit is inadequate for describing the charge transport physics of organic light harvesting systems. It is experimentally shown that the onset of the photocarrier recombination is determined by the electrode charge and we propose the mobility-recombination coefficient product as an alternative figure of merit. The implications of these findings are relevant to a wide range of light harvesting systems and will necessitate a rethink of the critical parameters of charge transport.

Monte Carlo studies of non-conservative electron transport in the steady-state Townsend experiment

An investigation of the spatial relaxation of the electrons and benchmark calculations of spatially resolved non-conservative electron transport in model gases has been carried out using a Monte Carlo simulation technique. The Monte Carlo code has been specifically developed to study the spatial relaxation of electrons in an idealized steady-state Townsend (SST) experiment in the presence of non-conservative collisions. Calculations have been performed for electron transport properties with the aim of providing the benchmark required to verify the codes used in plasma modelling. Both the spatially uniform values and the relaxation profiles of the electron transport properties may serve as an accurate test for such codes. The explicit effects of ionization and attachment on the spatial relaxation profiles are considered using physical arguments. We identify the relations for the conversion of hydrodynamic transport properties to those found in the SST experiment. Our Monte Carlo simulation code and sampling techniques appropriate to these experiments have provided us with a way to test these conversion formulae and their convergence.

The impact of hot charge carrier mobility on photocurrent losses in polymer-based solar cells

A typical signature of charge extraction in disordered organic systems is dispersive transport, which implies a distribution of charge carrier mobilities that negatively impact on device performance. Dispersive transport has been commonly understood to originate from a time-dependent mobility of hot charge carriers that reduces as excess energy is lost during relaxation in the density of states. In contrast, we show via photon energy, electric field and film thickness independence of carrier mobilities that the dispersive photocurrent in organic solar cells originates not from the loss of excess energy during hot carrier thermalization, but rather from the loss of carrier density to trap states during transport. Our results emphasize that further efforts should be directed to minimizing the density of trap states, rather than controlling energetic relaxation of hot carriers within the density of states.

Development of swarm transport theory in radio-frequency electric and crossed electric and magnetic fields

The advancements associated with modern day technology demands incorporation of the best physical understanding and the most accurate modelling of charged particle motion in gases. In recent times there have been major advances in the fundamental swarm transport theory, and this is the subject of the present paper. We start from 1986, when “multi-term” solutions of Boltzmann’s equation for static electric fields had been developed to a sophisticated level, and proceed through to the present day, where the theory is motivated far more by application to industrial processes, which involve both electric and magnetic fields , either static or time varying. We present a unified time-dependent multi-term solution of Boltzmann’s equation, emphasising the common methods and techniques underlying the treatment of all these situations, whether they be for electron or ion swarms. New and significant numerical results are presented to highlight the rich and diverse range of phenomena which are observed.

Low-energy electron and positron transport in gases and soft-condensed systems of biological relevance

We present a study of electron and positron transport in water in both the gaseous and liquid states using a Boltzmann equation analysis and a Monte-Carlo simulation technique. We assess the importance of coherent scattering processes when considering transport of electrons/positrons in dense gases and liquids. We highlight the importance of electron and positron swarm studies and experiments as a test of the accuracy and completeness of cross-sections, as well as a technique for benchmarking Monte-Carlo simulations. The thermalization of low-energy positrons (<150 eV) in water is discussed and the sensitivity of the profiles to the form of the cross-sections in this energy region, and assumptions in the microscopic processes, is considered.

Electron drift velocities in He and water mixtures: measurements and an assessment of the water vapour cross-section sets.

The drift velocity of electrons in mixtures of gaseous water and helium is measured over the range of reduced electric fields 0.1-300 Td using a pulsed-Townsend technique. Admixtures of 1% and 2% water to helium are found to produce negative differential conductivity (NDC), despite NDC being absent from the pure gases. The measured drift velocities are used as a further discriminative assessment on the accuracy and completeness of a recently proposed set of electron-water vapour cross-sections [K. F. Ness, R. E. Robson, M. J. Brunger, and R. D. White, J. Chem. Phys. 136, 024318 (2012)]. A refinement of the momentum transfer cross-section for electron-water vapour scattering is presented, which ensures self-consistency with the measured drift velocities in mixtures with helium to within approximately 5% over the range of reduced fields considered.

High-order fluid model for streamer discharges: I. Derivation of model and transport data

Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. This paper focuses on the derivation of a high-order fluid model for streamers. Using momentum transfer theory, the fluid equations are obtained as velocity moments of the Boltzmann equation; they are closed in the local mean energy approximation and coupled to the Poisson equation for the space charge generated electric field. The high-order tensor in the energy flux equation is approximated by the product of two lower order moments to close the system. The average collision frequencies for momentum and energy transfer in elastic and inelastic collisions for electrons in molecular nitrogen are calculated from a multi-term Boltzmann equation solution. We then discuss, in particular, (1) the correct implementation of transport data in streamer models; (2) the accuracy of the two-term approximation for solving Boltzmanns equation in the context of streamer studies; and (3) the evaluation of the mean-energy-dependent collision rates for electrons required as an input in the high-order fluid model. In the second paper in this sequence, we will discuss the solutions of the high-order fluid model for streamers, based on model and input data derived in this paper.

Transport coefficients and cross sections for electrons in water vapour: comparison of cross section sets using an improved Boltzmann equation solution.

This paper revisits the issues surrounding computation of electron transport properties in water vapour as a function of E/n(0) (the ratio of the applied electric field to the water vapour number density) up to 1200 Td. We solve the Boltzmann equation using an improved version of the code of Ness and Robson [Phys. Rev. A 38, 1446 (1988)], facilitating the calculation of transport coefficients to a considerably higher degree of accuracy. This allows a correspondingly more discriminating test of the various electron-water vapour cross section sets proposed by a number of authors, which has become an important issue as such sets are now being applied to study electron driven processes in atmospheric phenomena [P. Thorn, L. Campbell, and M. Brunger, PMC Physics B 2, 1 (2009)] and in modeling charged particle tracks in matter [A. Munoz, F. Blanco, G. Garcia, P. A. Thorn, M. J. Brunger, J. P. Sullivan, and S. J. Buckman, Int. J. Mass Spectrom. 277, 175 (2008)].

A multi-term solution of the nonconservative Boltzmann equation for the analysis of temporal and spatial non-local effects in charged-particle swarms in electric and magnetic fields

A multi-term solution of the Boltzmann equation has been developed and used to investigate the temporal and spatial relaxation of charged-particle swarms and associated phenomena induced by non-local effects under the influence of electric and magnetic fields crossed at arbitrary angles when nonconservative collisions are operative. The hierarchy resulting from a spherical harmonic decomposition of the Boltzmann equation in both the hydrodynamic and non-hydrodynamic regimes is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a variety of Maxwellian based weighting functions. Temporal and spatial relaxation profiles of various charged-particle swarm transport properties are presented for certain model and real gases over a range of field strengths and angles between the fields. It was found that the magnetic field strength and angle between the fields have an ability to control the relaxation process: in general, these parameters can be used to enhance or suppress the oscillatory features in the relaxation profiles of various transport properties. The explicit and implicit effects of nonconservative collisions on the drift and diffusion elements in varying configurations of radio-frequency electric and magnetic fields are considered using physical arguments.